@article {IOPORT.05956317,
    author       = {Buckwar, E. and Riedler, M.G. and Kloeden, P.E.},
    title        = {The numerical stability of stochastic ordinary differential equations with additive noise.},
    year         = {2011},
    journal      = {Stochastics and Dynamics},
    volume       = {11},
    number       = {2-3},
    issn         = {0219-4937},
    pages        = {265-281},
    publisher    = {World Scientific, Singapore},
    doi          = {10.1142/S0219493711003279},
    abstract     = {The $d$-dimensional semilinear stochastic differential equation with additive noise $$dX(t)= (AX(t)+ f(X(t)))\,dt+\sigma dW(t),\tag1$$ where $W(t)$ is a standard $m$-dimensional Wiener process and $A$ is a $d\times d$ matrix, is shown to be a more appropriate test equation for numerical schemes designed to approximate the solution of a stochastic differential equation with additive noise. Under specified stability conditions, it is proved that for all step-sizes $h$, the $\theta$-Maruyama scheme, the linear implicit Euler-Maruyama method, the explicit exponential Euler scheme of Lord and Rougemont, and the explicit exponential Euler scheme of Jentzen and Kloeden (except in this last scheme for $h\in(0, h^*)$, where $h^*$ is specified) have, when applied to equation (1), a unique stochastic stationary solution which is pathwise asymptotically stable.},
    reviewer     = {Melvin D. Lax (Long Beach)},
    identifier   = {05956317},
}